That’s right, and it’s not just funding. The government also has other ways of putting their foot on the scale. They can threaten, or incentivize private media by selective enforcement of regulations.
There is also a revolving door between government and media - whereby government and media collude, exchanging leaks, favorable coverage and even career opportunities in both sectors..
In the old days leftists liked to use the words “chilling effect” when government actions indirectly harmed freedom of speech.
The concept was valid—even the fear of lawfare or regulation is enough to silence or muffle most speakers.
Lawfare against speakers is de facto government action if it is allowed in the courts.
The Alex Jones and other cases set a precedent where anyone can claim they were harmed by another’s speech—even where no financial damage can be proved.
Continuing..one controversial (often non political) podcast I listen to has to used code-words all the time and openly say “we can’t say this directly or we will be banned”.